Question: Simplify the following expression: $t = \dfrac{2k^2 - 18k + 28}{k - 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $2$ , so we can rewrite the expression: $ t =\dfrac{2(k^2 - 9k + 14)}{k - 7} $ Then we factor the remaining polynomial: $k^2 {-9}k + {14} $ ${-7} {-2} = {-9}$ ${-7} \times {-2} = {14}$ $ (k {-7}) (k {-2}) $ This gives us a factored expression: $\dfrac{2(k {-7}) (k {-2})}{k - 7}$ We can divide the numerator and denominator by $(k + 7)$ on condition that $k \neq 7$ Therefore $t = 2(k - 2); k \neq 7$